Question: The following line passes through point $(5, 3)$ : $y = \dfrac{2}{13} x + b$ What is the value of the $y$ -intercept $b$ ?
Substituting $(5, 3)$ into the equation gives: $3 = \dfrac{2}{13} \cdot 5 + b$ $3 = \dfrac{10}{13} + b$ $b = 3 - \dfrac{10}{13}$ $b = \dfrac{29}{13}$ Plugging in $\dfrac{29}{13}$ for $b$, we get $y = \dfrac{2}{13} x + \dfrac{29}{13}$. ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${10}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${\llap{-}10}$ ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${10}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${\llap{-}10}$ $(5, 3)$